Question

Solve the triangle ABC, if the triangle exists. A = 44.5° a = 8.6 m b= 10.5 m Select the correct choice below and fill in the answer boxes within the choice. O A. There is only 1 possible solution for the triangle. The measurements for the remaining angles B and C and side c are as follows. mZB= mZC= The length of side c= (Round to the nearest (Round to the nearest (Round to the nearest tenth as tenth as needed.) tenth as needed.) needed.) B. There are 2 possible solutions for the triangle. The measurements for the solution with the longer side c are as follows. mZB- mZC- The length of side c- (Round to the nearest (Round to the nearest (Round to the nearest tenth as tenth as needed.) tenth as needed.) needed.) The measurements for the solution with the shorter side c are as follows. mZB- mZC- The length of side c- (Round to the nearest (Round to the nearest (Round to the nearest tenth as tenth as needed.) tenth as needed.) needed.) OC. There are no possible solutions for this triangle.

Answer 1

The solutions are given below

Q-1)In SinA triangle مسا know that SinB - Sinc a C -Taking first two terms, we عليا Here given that A=44.5°, a= 8.6 and b2 10.5 Sin 44.5 Sin B Sly C 10.5 have Sin 44.50 Sin B. 8.6 10.5 or Sin B 10.5. Sin 44,5 8.6 » SinB 0.855761301 B = Sint (0-855761311) B 50.843943 Or B = 121.1560 57 B = 50.8° 121.2° And know that A+B tc=100 C = 100-44.5-50.0 or. C=100-44.5-121.2 C 76.70 c=14.3° so So, it C = 76.7° rom Sin 44.5 = Isin 76.7 с C=0.6) Sin 76.7 Sin 44.5' ( = 11.9406 or c= Or Ον 3 لیا 0.6 11.9 m And it C-14.30 So sinu4.5 Sin 14.3 8,6 С. C = (0.6) Sin 143 Sinyys = 3.030622 OY c=3 m

Thus, the triangle has two solutions longer Iside a m<b=58.80 m<c= 76.7°, Coll. 9m C with shorter side m<B=121.2° m<C= 14.3° c=3m Q-2) The given equation is 2 =0 -21032k=3losat1 20032x+3losx tl=0 21082x +200sxtcosx t1 = > 2605x(cosx tu t(65x H) = 0 20038ti) (Cssxtu). Cos X=- cosa =-| OY And we know that cosa=-l at x=yt and a= 27 2 3 3 And cosx=-l at a=t over the internal (0,27) Thus, the solution set of equation is solution set is is 277 A A}